Double parabolic cylinder pencil beam antenna



R. c. SPENCER 2,825,063

DOUBLE PARABOLIC CYLINDER PENCIL BEAM ANTENNA Feb. 25, 1958 3 Sheets-Sheet 1 Filed Nov. 20, 1953 R. c. SPENCER 2,825,063

DOUBLE PARABOLIC CYLINDER PENCI L BEAM ANTENNA Filed Nov. 20, 1955 Feb. 25, 1958 3 Sheets-Sheet 2 INVENTOR. F07 C fif/VKZE BY yaw/ i Feb. 25, 1958 R. c. SPENCER 2,825,063

DQUBLE PARABOLIC CYLINDER PENCIL BEAM ANTENNA Filed Nov. 20, 1955 3 Sheets-Sheet 3 Fifi INVENTOR; F0) 6'. 5Pf/VZE8 (15M T- [ML-4 tr ted tates Patent ce 232M v Patented Feb. 25, 1958 This surface is so oriented that: (1) its focal line coincides with DD, (2) it contains the point F, and 2825 063 (3) any ray emitted radially from DD' is reflected parallel to the positive z axis. Under these conditions, DOUBLE PARABOLIC CYLINDER PENCIL BEAM 5 S has the same focal length as S and the point V, AN NNA with coordinates (f, 0, f) lies on the vertex line Roy (3. Spencer, Arlington, Mass.

Application November 20, 1953, Serial No. 393,527

6 Claims. (Cl. 343837) (Granted under Title 35, U. S. Code (1952), see. 266) The invention described herein may be manufactured and used by or for the Government for governmental purposes without payment to me of any royalty thereon.

This invention relates to microwave antennas and particularly to such antennas for projecting a narrow beam of radiant energy from a point source.

The usual microwave beam antenna allows energy from a point source to reflect from a paraboloid of revolution so that the outgoing energy travels in lines parallel to the axis of revolution of the paraboloid. The antenna forming the subject matter of this invention produces a similar beam of energy, however, instead of using a paraboloid of revolution as a reflector, use is made of successive reflections from two parabolic cylinders with straight-line elements at right angles, each cylinder collimating the beam in one plane.

An advantage of this design is that the reflecting surfaces may be simply and inexpensively stamped or cut from flat sheets, with packaging, storage and shipment being facilitated by the flat form of the reflecting cylinders. A further advantage of the design is the possibility of independent control of the vertical and horizontal beam widths. The beam from a point source can be broadened by warping the reflector slightly. The reflector with horizontal straight-line elements controls the vertical beam width and the reflector with vertical straightline elements controls the horizontal beam width. A second method of controlling the beam width is to change the relative position of the feed and one of the reflectors.

Although this invention particularly relates to microwave antennas the principles involved are equally applicable to light reflectors.

The invention will be described in more detail in connection with the specific embodiment thereof shown in the accompanying drawings, in which Fig. 1 shows the geometry of the antenna reflecting surfaces;

Figs. 2 and 3 show the developed curves of intersection in each surface, and

Figs. 4, 5, 6 and 7 show various views of a practica embodiment of the antenna.

Referring to Fig. 1, this figure shows a perspective view of the two parabolic cylinders making up the antenna reflectors. The first cylindrical surface S; is given by the equation.

where f is the focal length and L=2f is the semilatus rectum. The point F with coordinates (f, 0, 0) lies on the focal line of. S The line DD is the image of the point P in 3,, that is, any ray emitted from F and in cident on S at P is reflected as though it originated on DD.

The formula for the second cylindrical surface S is given by the equation:

HH of S it is evident, therefore, that any ray FP P emitted from a point source located at F will, after successive reflections from S and S be directed parallel to the positive z axis. If either condition (2) or condition (3) on S are relaxed, then other combinations of relative focal lengths and orientations would be possible while still satisfying the condition that the image of F in S coincide with the focal line of S It is thus possible for the two parabolic cylindrical reflectors to have different focal lengths and for the two surfaces to rotate relative to each other through some small but finite angle about line DD. It is not necessary for the source point P to lie on S however, it can be made to do so by appropriate culated using Equations 1 and 2. The curve of inter-- section may be written in the following parametric form- Table 1 below contains numerical values of x, y and z as computed from Equation 3. The range of z (i. e., y) is from 0 to 2 in increments of 0.1.

Table 1 Point N o. t z y 2 s 8g The curve of intersection of the two surfaces S and S is a threedimensional space curve denoted as C in Fig. 1. If the surfaces S and S are separately developed into planes, the intersection curve in each case becomes a plane curve. However, these two plane curves are not identical. In the construction of the double cylindrical reflector, it is desirable to know the coordinates of these plane curves so that they may laid out on flat sheets before the sheets are bent into the parabolic cylindrical shape.

Curves of z=constant in the surface 8 are all identical parabolas and s is defined to be the arc length along any of these parabolas as measured from the z axis (see Fig. 1). Similarly, the curves of y=constant in the surface 8,. are all identical parabolas and s is defined to heme arc length along any of these parabolas as measured from the vertex line HH. Table 1 gives the x, y and z coordinates of the intersection curve C. In order to obtain the s 2 coordinates of C as measured in the surface-S it is necessary to determine s as a function of either 1 or y, i. 6., the arc length of a parabola as a function of its coordinates. Similarly, in order to obtain the s y coordinates of C as measured in the surface 8;, it is necessary to determine s, as a function of either A or z. The last two columns of Table 1 give parabolic arc lengths as taken from Air ForceCambridge Research Center Report No. E4983,- July 1951, A Table of Normalized Parabolic Coordinates and Arc Lengths, by R. C. Spencer and G. E. Reynolds.

The straight-line elements of the cylinder S along which the z coordinate is measured, together with the parabolas along which s is measured, form an orthogonal curvilinear coordinate system on the surface 8,. When the cylinder is developed into a plane, this coordinate system becomes a rectangular system in the plane. The z coordinatesof the intersection curve C are given in Table 1 and a plot of this curve on the developed surface S is showninFig. 2. Similarly, the cylinder S contains an s y orthogonal curvilinear coordinate system that becomes arectangular system when S is developed into a plane. The s,, y coordinates of the curve of intersection are given in Table l and a plot of this curve on the developed surface S is shown in Fig. 3. Note that certain points along the intersection curves, as shown in Figs. 2 and 3, are numbered according to the first column of Table 1. When the developed surfaces S and S are returned to their parabolic cylindrical form and fitted together, identically numbered points will coincide.

A practical embodiment of an antenna constructed in accordance with the foregoing principles is shown in Figs. 4', 5 and 6 in assembled form. Fig. 7 shows the antenna disassembled which illustrates the advantages of the design from the standpoints of packaging, shipping and storing.

The assembledantenna comprises two V-shaped side pieces 1 and 2 separated on one side by struts 3, 4 and 5 and onthe other by parabolically curved struts or ribs 6 and 7. The ends of the struts and ribs are provided with dowel pins which pass through openings in the side pieces and are fastened by slide fasteners 8 as shown. The twolongerlegs of the V-shaped side pieces 1 and 2 are provided with slots 9 and 9' which conform to a These slots receive the edges of the sheet metal reflector S and hold it in parabolic cylindricalform with the straight-line elements ofthe reflecting surface normal to the slots; Reflector S is held in position parabolic curve.

by reflector support bar 10 and locking screw 11- which passes through a hole in S (Fig. 7). The bar1'0' is held in position between the side pieces 1 and 2-by dowels are in the slots it is held in parabolic cylindrical form with the straight-line elements of the reflecting surface parallel to the'slots. The inner edges of'ribs 6 and'7 are curved parabolically to conform to the shape of reilector S The horn-feed and wave guide assembly 13 is remov'ably attached to struts 4 and 5 by means of dowel pins andslide fasteners thehorn-extending-through an opening in S I claim:

1. A radiator comprising a pair of parabolic cylindrical reflecting surfaces S and S said surfaces being positioned relative to each other so that their straight-line elements are at right angles and so that the focal line of S coincides with the image in S of a point P on the focal line of S and a point source of radiant energy located at F and directed toward S 2. A radiator comprising a pair of parabolic cylindrical reflecting surfaces S and S having equal focal lengths; said surfaces being positioned relative to each other so that their straight-line elements are at right angles, so that the focal line of S intersects S at a point P, and so that the focal line of S coincides with the image of the point P in S and a point source of radiant energy located at F and directed toward S 3. A radiator comprising a pair of intersecting parabolic cylindrical reflecting surfaces S and S having equal focal lengths; said surfaces being positioned relative to each other so that their straight-line elements are at right angles, so that the focal line of S intersects S at apoint F; and so that the focal line of S coincides with the image of the point F in S and a point source of radiant energy located at F and directed toward 8,.

4. A radiator structure comprising a pair of V-shaped sidepieces and strut members therebetween for supporting said sides in parallel spaced relation; means providing a pair of oppositely disposed slots in one pair of oppositely disposed legs of said V-shaped sides, said slots conforming to the curve of a parabola; means providing a pair of oppositely disposed straight slots in the other pair of oppositely disposed legs of said V-shaped sides; saidslots in both pairs of oppositely disposed legs lying inside said strut members; a first sheet of metal supported at the edges by said parabolic slotsand held in parabolic cylindrical form thereby with the cylindrical straight-line elements normalto and terminating in said parabolic slots; a second sheet of metal supported at the edges by said straight slots, the dimension of said second sheet at right angles to' said straight slots being greater than the distance between said straight slots, and the struts behind said-straightslotsbeing shaped in the form of a parabolic curve; so that" said second sheet is pressed against said curved struts to form a parabolic cylindrical reflecting surface the straight-line elements of which are parallel to said straight slots; and a point source of ra-diantener'gy located on the concave side .of said second sheet and'directe'd towardsaid reflecting surface.

5. Apparatus as claimed in claim 4 in which said source of radiant energy is the open end of a waveguide.

6. Apparatu'sas' claimed in claim 4 in which said point source is located at apoint on the focal line of said refleeting surface formed by said second sheet and in which theshape o'f-said parabolic slots, the width of said second sheet and the shape of said curved struts, and the angle of said V" are such that the focal line of the surface formed by said first sheet coincides with the image of said point'of location of said source with regard to the reflecting surface formed by said second sheet.

References Cited in the file of this patent UNITED STATES PATENTS 2,160,853 Gerhard June 6, 1939 2,579,140 Crawford Dec. 18, 1951 2,597,391 Sichak May 20, 1952 FOREIGN PATENTS 576,941' Great Britain..- Apr. 29, 1946 577,939 Great" Britain June 6', 1946 

